A little over half way through this essay, I express the importance of first asking “What is it?” when delving into an inquiry. In other words, what category does whatever one is examining fall into? We wouldn’t want to use a hammer where a pipe wrench is called for. And we wouldn’t understand poetry if we read it simply as prose. Even words fall into categories (past tense versus present tense, for example) and essays also fall into categories. So, what is it that we have before us? I believe the reader is entitled to an answer to that question right from the beginning, before committing to reading a lengthy presentation on critical thinking. Not only is the question of category important when deciding whether to read the essay, the question is even more important when attempting to understand what it is we are reading.
When considering the answer to the question “What is it?” with regard to the following pages, the word “kit” comes to mind. The information presented here should be looked at as a “starter kit” and a “tool kit”. It is not a comprehensive presentation on how to think since such an endeavor would consist of several volumes. It is meant to be brief, handy and practical. Something a person can carry around in her head and use at a moment’s notice.
If the reader gets lost or bored or frustrated with the content in any given section please feel free to skip over the detail and explanation being given. Try to take away from the essay the general idea, the big picture of what is being presented. For example, if formal logic is not your “cup of tea” at least understand that a truth claim should be supported by other truth claims that follow some rule of logic. Or if math is not your strong point understand that asking “what are the odds” is generally a good thing to do but that this question is not always applicable.
I have herein often sacrificed literary style to achieve brevity believing that many a reader is “put off” by lengthy discussion and superfluous explanation. It is also in keeping with the methodology encouraged here, that of getting to the point and telling the reader why he or she should believe it. It is meant to be something like fatherly advice, a few clues to finding and using wisdom for a happy, healthy life and for a better world. All this in so few pages? Let’s see to what extent that goal is achieved.
The Preeminence of Thought
Why think? To find truth, to find freedom, to avoid pitfalls, to find happiness, to find God, to help others.
What about feeling, emotion, caring? Emotion and caring are not antithetical to thinking. Generally speaking, thought precedes emotion, in other words, we think something and then we feel something. We can’t always put our thoughts into words and often our thoughts are not clearly formed, but generally speaking, we think something and then we may feel something and then we may do something. This is often the definition of a person: mind, will and emotion.
If someone thinks they are in danger (justified or not), they feel fear. If someone thinks people are animals, that person may very well treat people as animals. The person who believes people are God’s special creation, made in God’s image, in a sense, sacred, that person is more likely to treat them as inviolate, sacred and not as animals. In a sense, we are back to the importance of knowing what category things (and people) fall into. Categories are fundamental to clear thinking. People who tend to blur the distinctions between categories should be seen as suspect. Either their thinking is confused, or they want to confuse the listener or reader. Oftentimes they are both confused and wanting to confuse others.
There may be some “primal” emotions like sympathy or empathy, love or hatred, or fight or flight where very little thinking is involved (an emergency requiring immediate action) but even there some thought precedes emotion, decision and action. Even foolish actions are preceded by thought, erroneous thoughts like “there will be no consequences”.
Thinking skills are a lifetime endeavor. Experience is a great teacher. Some experiences are very costly teachers. Parents, due to their age, generally have experience and knowledge. They cringe and worry over some things their children are walking headlong into. They often wish their children would think before they act. The purpose of this study is to outline a few of the major points on the importance and the methodology of reason.
People who are led by emotion without thinking or who act before they think or whose thinking is not in accordance with truth often find themselves victims of swindlers, manipulators, abusive spouses, bosses or dictators. The Devil is the deceiver. Eve was deceived (2 Cor. 11:3). The world is under the power of the deceiver (Rev. 12:9).
The best defense against deception is critical thinking. One of the first steps in critical thinking is a healthy skepticism, an understanding that we belong to a fallen human race (we are all sinners) and we all have our biases, self-interest and agendas. A corollary to the fallenness of humanity is that many things in life and the world of human action and interaction are probably wrong or flawed in some way. The wise person will just expect it. Sounds awfully pessimistic but that is reality and it is also the biblical view of the world. Understanding not only that things are apt to go wrong in life but also that many things will actually be wrong, morally wrong, may well be the beginning of wisdom and the beginning of a happier, healthier and saner life.
The New Testament uses the word “believe” dozens of times as the beginning of the cure for a fallen world. Belief, in the biblical sense, is commitment to what one has been persuaded is true, based on evidence and reason. The commitment that comes from being persuaded by the evidence and arguments should lead to some kind of emotion and action. Belief in the biblical sense means thinking using the patterns, claims, categories and conclusions found in the Bible. And it is a justified belief.
There is such a thing as justified belief. A person can be said to be justified in her belief
- if there is evidence supporting it
- if there are arguments supporting it
- if the arguments are free of internal and external contradictions and logical fallacies and
- if she has examined the counterarguments and diverse beliefs held by others. Always ask to look at the minority report, see what the opposition is saying. This methodology must become second nature. It must be developed and exercised continuously.
Failure to insist on having evidence, sound argument and exposure to counter arguments leaves one open to being influenced by gossip, slander, deceit and manipulation.
One more important aspect of critical thinking that is often overlooked: keep and open mind. Don’t jump to conclusions. Don’t quickly assume you have the answer. Be aware of your own biases and presuppositions. Don’t brush aside ideas or claims simply because your mind is made up or because most people believe otherwise. Recognize that what “everybody knows” is often cultural conditioning, group think or thought reform. It’s also just natural for a person to believe things that are to their own advantage or that fit their preconceived notions. Remember, oftentimes the easiest person to fool is yourself.
So, in conclusion, thinking is fundamental to finding truth, freedom, happiness and God and to helping others do the same.
We begin our study of critical thinking with an easily understood set of ideas that apply not only to the physical world, but often even to the realm of ideas.
John Stuart Mill, a British philosopher, political scientist and economist (also a thoroughgoing atheist) in 1843 published his work on induction. The following is a concise summary of his findings that are still used today and that are very helpful in doing some forms of inductive reasoning. Mill’s methods are an easy place to begin our analysis of thought since they are very intuitive and common, yet often overlooked.
- The method of agreement. If two events are generally found to occur together or one after the other they are probably related in a causal manner. Example: Years ago, in the United States, it was noted that some cities had a remarkably lower incidence of tooth decay. These same cities, for some reason, had considerably higher concentrations of florine in their water supplies. Sure enough, when other cities began adding florine to their water, their rate of tooth decay declined dramatically. In the arena of thought, atheism and nihilism are often seen coupled together and efforts to disassociate the two seem unpersuasive to many. Is there a connection here?
- The method of difference. This method of inductive reasoning focuses not on what is common in various circumstances but on what is different. It could very well be called the method of subtraction. Yellow fever is a viral disease that has killed millions of people in tropical and sub-tropical Africa and South America. When rooms that were completely shielded from the presence of mosquitoes were provided, no one sleeping and working in those rooms during the experiment contracted Yellow Fever. By eliminating the mosquitoes, the disease was eradicated from those people protected from exposure to mosquitoes.
- The Joint method of agreement and difference. 1037 children in Kiryas Joel, New York, were vaccinated against Hepatitis A. Around 500 of the 1037 children were given dummy injections, injections not containing the vaccine. Of the 500 or so that received the vaccine not one child later contracted the disease. But very soon, 25 children came down with the disease, all from the group who had not received the vaccine. The agreement or commonality among the vaccinated children of not one case of the disease and the difference noted among those who had not been vaccinated definitively showed that the vaccine was effective.
- The method of residues. Any circumstance includes various elements. A grouping of suspected causes often contains various elements. To find the one cause of the circumstance in question one can proceed by eliminating from the list of possible causes those that are produced by known or soon discovered causes. A simple case is the tare weight of a truck. The tare weight is the weight of the unloaded truck, in other words the weight of the truck alone. Knowing the tare weight, a loaded truck can be weighed (on the highway, for example) and the weight of the cargo can be determined without unloading the truck. The weight of the cargo is the weight of the loaded truck minus the tare weight of the truck. So, if you have a list of possible causes and a list of possible results, you can sometimes find the cause or causes of some particular result by matching causes and effects and eliminating them. What is left is probably the cause or causes of the remaining results.
Another example is your car not starting. Possible causes include 1) no gas, 2) no spark, 3) faulty starter motor, 4) dead battery, 5) faulty alternator not charging the battery. By eliminating each possible cause one by one it is possible to arrive at the cause of the problem, fix the problem and then start the car.
- The method of concomitant variation. If one thing increases or decreases and something else increases or decreases (every time or most of the time) even with some time delay, then there is probably a connection between the two phenomena. An obvious example are the ocean tides and the phases of the moon. People who are deprived of sleep suffer more accidents or commit more errors. The less sleep, the more accidents or errors. There seems to be a causal relationship between lack of sleep and auto accidents.
The Limitations of Mill’s Methods
Mill’s Methods can be very powerful tools in determining cause and effect but are insufficient by themselves. In most cases the possible causes are very many indeed, as are the possible effects. What is needed prior to applying the methods is a hunch or suspicion or some inside information that eliminates or limits the number of possibilities. Also, all of the methods rely on observation. It isn’t possible to observe all cases or all trials. So, the conclusions are never 100% certain. That is typical of any kind of induction and is not surprising. Mill’s Methods do not lead to proofs but are very powerful tools in testing hypotheses.
As an example of the limitations of Mill’s Methods, in a debate on Politicon between Ben Shapiro and Cenk Uygur, Mr. Uygur cited the amazing prosperity experienced in the United States in the decades following World War II. He attributed that prosperity to very high corporate taxes during that same period or, at least, claimed that high corporate taxes do not impede general prosperity. Shapiro pointed out that after the Second World War the United States was the only Western economy still standing and not needing major rebuilding and thus was in an excellent position to succeed over its competitors. In other words, correlation was not causation and the end of the war placed the United States in an extraordinary position not seen since.
Here’s a humorous example that will help fix the limitations of Mill’s Methods in our minds. A certain man finds that bending his elbow ten or twelve times after work “causes” him to become inebriated! When he stops bending his elbow the problem goes away. Is it the bending of the elbow that causes inebriation?
Usually circumstances have multiple causes and the effect of any one of them is very difficult to ascertain. Debaters and persuaders often cite causal relationships that are very difficult to evaluate or even substantiate. They also ignore or are ignorant of other contributing factors or purposely fail to mention them. Remember, people tend to push their own agenda. They very seldom consider other options and often do not want you to consider other options.
A quote from Nobel Prize winning Physicist Richard Feynman illustrates what an honest, disinterested scientist should look like. Here it is from Feynman’s 1974 commencement address at Caltech.
“a kind of utter honesty—a kind of leaning over backwards. For example, if you’re doing an experiment, you should report everything that you think might make it invalid—not only what you think is right about it: other causes that could possibly explain your results; and things you thought of that you’ve eliminated by some other experiment, and how they worked—to make sure the other fellow can tell they have been eliminated…. In summary, the idea is to try to give all the information to help others to judge the value of your contribution; not just the information that leads to judgment in one particular direction or another.”Nobel Prize winning Physicist Richard Feynman
An important class of critical thinking is induction. Induction has to do primarily with probability or statistics. For example: Joe is Italian. So, Joe probably loves pasta and tomato-based sauces. Yes, probably. But not necessarily. We formulate many opinions and make many decisions based on probability. Insurance rates and medical treatments are often based on probability and statistics.
The fundamental idea behind probability is the ratio (fraction) of the number of favorable outcomes divided by the number of total possible outcomes. Example: A coin has two sides. In a coin toss there are two possible outcomes, heads or tails. The probability of getting a heads is ½ because there is only one way of getting a heads and there are two possible outcomes, heads or tails. In rolling a single die, there are six possible outcomes (six-sided die). There is only one way to get a four when tossing a single die. So, the odds of getting a four are 1/6.
In rolling two dice there are 36 possible outcomes. Six outcomes for the first die and 6 outcomes for the second die. 6 x 6 = 36. This simple observation gives us great insight into probability. Increasing the number of independent factors, (you have two dice rather than just one) greatly increases the number of possible outcomes and an increase in the number of possible outcomes greatly reduces the probability of any specific outcome. Another important observation is that specificity greatly reduces the number of favorable outcomes. When you have very specific qualifications for your outcome you have a very low probability of a success if the process is in any way random.
There are six ways of getting a seven (1,6) (6,1) (2,5) (5,2) (3,4) (4,3). So, the odds of getting a seven when rolling two dice is 6/36 or 1/6 or 0.16666667 or about a 17% chance.
Since probability can be seen as a ratio between the number of favorable (or desired) outcomes divided by the number of total possible outcomes, finding ways to simplify counting outcomes becomes very important. For example, how many ways are there of choosing three numbers, without repetition, from the numbers 1,2,3,4,5,6? The answer is 20, if the order doesn’t matter and 120 if the order does matter. If the order doesn’t matter, then 123 is the same as 132,213,231,312,321 and the same is true for any three-number combination that is chosen. So, in this example, for each three-letter combination of numbers there are six permutations. The 120 permutations must be divided by the six “copies” and you come up with only 20 combinations.
This example illustrates the vast difference in the number of possible outcomes we encounter depending on whether the order of the outcomes is important. When the order doesn’t matter we are looking at combinations, when it does matter we are looking at permutations. If you are dealing with a random process (like tossing dice or biological evolution) and the order of the outcomes is essential, the probability of a specific outcome becomes very, very small, very quickly.
This illustrates the fact that high specificity means low probability. Remember that a relatively large denominator or a relatively small numerator means low probability. For example, there are 2,598,960 possible five-card poker hands (this would be the denominator in the fraction). Only four of them are royal flushes (this would be the numerator), so the probability of getting a royal flush is 4/2,598,960 or one in 649,740 hands.
Generally speaking, probability deals with random outcomes like tossing two dice or flipping a coin or getting a certain poker hand. Insurance rates are based on the odds of someone having an auto accident or of having their house burn down. Insurance companies gather data on how many cars travel how many miles in a given geographical area and how many accidents there are in a given time period and how much each accident cost to repair, etc. They then base their rates on the odds of someone of a certain age, driving a certain kind of car, a certain number of miles per month in a certain area with so many accidents per month and so forth. Based on the answers to those statistics they calculate how much to charge for their insurance coverage and still make a profit. The company doesn’t know which driver will have an accident. But they calculate the odds of any random driver having an accident and go from there.
Crime detection and convictions often depend on “the odds”. When two men died of ethylene glycol (antifreeze) poisoning five years apart, police were suspicious because these two men “just happened” to be married to the same woman at the time of their deaths. The woman also “just happened” to collect sizeable life insurance payments in both cases. This, in itself, wasn’t enough to convict her. But when the jury was told she continuously lived a lifestyle way beyond her means and had told the bank three weeks prior to her husband’s death that “everything will be alright in a week or two” and when her husband’s fingerprints were not found on the glass containing the antifreeze but hers were, she was convicted of double homicide. Criminal detection and conviction are great examples of arriving at a conclusion based on cumulative evidence and probability thinking and will be analyzed in more detail below.
Many issues involving critical thinking fall into the area of probability or statistics. It is generally a good idea to ask, “What are the odds?” The odds are not good when looking at something that either has a lot of possible outcomes (a large denominator) or very few favorable outcomes (a very small numerator). This is, in a nutshell, the application of probability or statistics to critical thinking.
Improbable things do, infrequently, happen. So, we can’t conclusively say that an event that has a small probability of occurring did not or does not take place. Nor can we assume that the occurrence of an event with a small probability was necessarily the result of design or intentionality (and was, therefore, not random).
William Dempski, in his 1998 book “The Design Inference” has suggested that we can know with near certainty that some event was the result of intentionality and intelligence if the event is complex (has many parts or elements to it) and if it is specific (corresponds to some completely unrelated complex pattern). Like finding “John loves Lucy!” carved onto the bark of a tree. In this case the phrase “John loves Lucy!” has seventeen characters (including the two spaces). It is somewhat complex. It also corresponds to an English sentence. English is not connected in any way to that tree or any tree. It is an independent source, an outside source. That is enough to believe intentionality is involved. Dempski called it “complex specificity”
Note 1: In apologetics, Christians often cite the odds of another planet like earth existing in the universe as infinitesimally small. That is because the odds of a planet orbiting a single star like our sun, at the right distance from the star, having the right planet mass to retain an atmosphere, having the right kind of atmosphere, containing a magnetic field, having liquid water in abundance, revolving around its axis in a suitable time frame, being protected from asteroids by a massive planet like Jupiter and many other necessary factors for sustaining life (no fewer than 20) are very, very small. The fact that there are trillions of stars in each of trillions of galaxies doesn’t come close to making another planet like earth at all probable. Added to this probability argument is the failure of the best minds on earth to come up with a plausible explanation of how life came into existence even on this planet that, surprisingly and unexplainably, satisfies all the factors needed to sustain life.
Note 2: The notion of probability is very important because many atheists are “philosophical materialists” . That is, they believe life, reality and the entire universe are simply results of random processes. They believe there is no God, no soul, no mind, no spirit. There are only molecules, energy, force fields, random actions and physical laws. Atheists have been known to ask, “What are the odds that God exists?” The question seems to imply that God is a product of random processes. Remember, probability has to do with random events or at least a ratio of favorable outcomes divided by total possible outcomes. Christians don’t claim that God is the result of random processes and so the atheist’s question seems misdirected and nonsensical.
Note 3: They also argue the following: There are so many supposed “gods” like Zeus, Odin, RA, Osiris, etc. How can one possibly know which one is the “true god”? Answer: In the same way a rational person decides which house or car to buy or which witness to believe in a court of law. By looking at the evidence, arguments and counter arguments.
Note 4: The lottery. I’ve had atheists say that even though the odds of winning the lottery are very slim, someone always wins the lottery. So, our planet and life are not necessarily unusual! Actually, the odds of “someone” winning the lottery are usually 100% since some number will be drawn and that number will be the winner. The odds of knowing who will win the lottery before the drawing takes place or believing that you will the win the lottery when you buy the ticket is another matter. In other words, specifying the winner before the drawing, while there are millions of possible outcomes and only one favorable outcome becomes very unlikely.
Note 5: Probability is based on what we know. We know a coin has two sides and a die has six. We can count or calculate the number of favorable and possible outcomes for a five-card poker hand. We have to know something before even seriously talking about probability. The more we know the better our estimate of the probability will be.
Note 6: Another unfounded argument by atheists against the claim that life and the universe seem designed is this: “We only know one universe. That is a very small sample size. Generally, in statistical analysis, you want a large sample size.” One response to this would be to point out that you don’t need dozens of coins to realize that the odds of a heads is ½ or that the odds of getting a four on rolling a die is 1/6. Perhaps that is the difference between probability and statistics. Also, the apparent fine tuning of the universe is based on what we know about the universe much like what we know about a coin or a set of dice. If you know the number of favorable outcomes and the number of total possible outcomes, you will have a pretty good grip on the probability of any given outcome.
The study and application of probability theory to the issues of life is very helpful and, in many cases, indispensable to finding truth. It is a branch of Mathematics and the fact that many students are not exposed to it is an interesting commentary on what the American “educational” system is all about. Can it be that our government-run educational system doesn’t really want an educated, critical thinking American population? I’m not talking about the thousands of dedicated, hard-working individual classroom teachers. I’m questioning the political and governmental agencies that determine the curriculum and basic methodologies behind what takes place in the classroom. Oh, there I go again, doubting the good, disinterested intentions of others and expecting the world to be wrong on almost any issue. But remember, that is what critical thinking is all about!
Our brief inquiry into the mathematics of probability is far from comprehensive, but the above introduction will hopefully give the reader a good foundation to critical thinking and the role that numbers often play in finding truth (or at least signaling caution). In the course of this study I will frequently encourage to reader to question the claim (any claim). When applicable, the question “What are the odds?” or the demand to “give me the numbers” is a great start.
Let’s now move on to other methods of finding truth, freedom, happiness and God and to helping other do the same.
The Cumulative Argument
Former Torrance, California cold-case homicide detective turned Christian James Wallace has written a book entitled “Cold Case Christianity”. In the first half of the book he outlines the kind of thinking that a good detective needs to utilize in order to correctly solve a mystery event of the past. Much of what Wallace says about solving homicides is applicable to thinking in general. Let’s see what Wallace has to say.
- Keep an open mind. Be aware of your own biases (and the biases of others) and do not limit the outcome to foredrawn conclusions. Objectivity is paramount. People are often incapable of even understanding another person’s perspective or opinion because their worldview excludes certain ideas from the realm of possibility. For example, the thoroughgoing philosophical materialist cannot, literally cannot, understand concepts such as the soul, spirit, god or the afterlife. I’ve seen this type of atheist nearly scream in frustration when someone mentions any of the aforementioned words. They simply cannot tolerate anyone bringing concepts involving the non-material (like soul or afterlife or, God forbid, God) into the conversation. They have already excluded such possibilities from consideration. Our point here is to keep an open mind.
- Learn to infer. To infer is to come to a conclusion based on evidence, arguments and counter arguments. Wallace calls this abduction or choosing the best explanation from a list of possible explanations. One can know the best explanation because the best explanation will 1) have explanatory viability (it will be possible), 2) explanatory simplicity (it will usually be straightforward), 3) explanatory depth (will it account for the greatest amount of evidence), 4) explanatory consistency (it will have the least or least serious contradictions or difficulties) and 5) explanatory superiority (it will best explain the who, when, where, how and why of the data gathered in the discovery phase of the investigation).
- At times one will simply have to fall back on the “minimal facts approach” where one gathers together only the facts that everyone agrees upon and sees what explanation best fits those minimal facts.
- Look for the cumulative case. Don’t expect or insist on absolute proof. Rather, approach questions by building what is known in forensics as a circumstantial case. Try to put together the little, sometimes seemingly insignificant, pieces of the puzzle in order to build a case for or against a conclusion.
- Examine your witnesses. A crime detective understands that a number of witnesses to a crime will exhibit the following: 1) their statements will flow from their individual perspectives, like their different physical locations at the scene. So eye-witness testimony will be perspectival, 2) observations will be idiosyncratic, that is, their observations will follow or favor their individual interests or expertise, and 3) their account will naturally have points in common and individual differences, in other words, they won’t agree on every detail but they should agree on some. This is important when examining historical documents like the accounts of the life, death and resurrection of Jesus. Many critics doubt and encourage others to doubt the accounts because they themselves overlook the observations noted here.
We may not ever be homicide detectives, but, these principles are an absolute necessity for anyone wanting to find truth, freedom, happiness, God and to help others do the same. For example, when reading a book or listening to a debate, we need to keep an open mind, demand evidence, arguments and counterarguments and see if the author or debater has presented a sound case for her position. And if we want to honestly persuade others we need to do what we expect others to do.
Learning to ask questions
An important aspect of finding truth is asking questions. We ask questions for clarification and for acquiring sufficient information to enable us to evaluate the strength of an argument or the veracity of a truth claim. A key component to critical thinking is the ability to ask questions like a detective.
The following is an example of how a detective might interrogate a suspect or witness in an attempt to discover if the suspect or witness is telling the truth. It is fairly easy to fabricate a story when the story contains few details. One sign of a true account is a wealth of detail. Someone once said, “The Devil is in the details”. Details are what trip people up when they are being deceptive or simply when they are mistaken because each detail must fit into the narrative without contradicting other parts and each detail must form part of one consistent whole. So, the detective will ask for as many details as he or she can.
When talking to non-believers, especially those who actively oppose Christianity, the ability to ask relevant questions is a very helpful skill to have. As in all skills, practice makes perfect. You can begin practicing by doing the assignment on the next page. Here’s the example offered as a starter from our imaginary detective.
Detective: Where were you on the morning of April 7th at 10 a.m.?
Suspect: I went fishing.
Detective: Where did you go fishing? Did anyone go with you? Did you catch anything? What did you use for bait? Where did you get the bait? Do you have a fishing license? What kind of fishing pole do you have? How long have you had it? Where did you buy it? What color is it? Do you have a spinning reel or a casting reel? What was the weather like? Did you stop along the way anywhere? How did you get to the fishing spot? What time did you get there? What time did you get back home? Was anyone home when you arrived? Did you rent a boat? Do you fish there often? Does anyone ever go fishing with you or do you always go alone? Did you talk to anyone later about your fishing that day? What did you tell them? Did you cook the fish right there or did you take it home? Did you take any photos that day? Did you have your cell phone with you that day? Did anyone call you while you were fishing? Did you call anyone?
For the detective, the more details that can be verified or corroborated the better. It would take an exceptional liar to be able to invent all the details involved in answering all of these questions and the invented answers would pretty certainly not withstand scrutiny. This is the type of technique we need to use when talking to a Buddhist, Atheist, New Ager, Mormon, JW, Darwinist or anyone else. And this is the type of questioning we need to be able to respond to when defending the Christian Faith!
Take the time to devise questions for the Atheist, New Ager, Darwinist, Buddhist, Muslim, cult leader and cult follower ahead of time so that when the occasion presents itself, you are prepared.
The first step, as always, is to ask a question, get a statement and then begin to ask more questions that will either verify or falsify the statement.
What is it?
The above discussion highlights the importance of looking for the details. The more details one has the easier it is to spot contradictions, errors or deception. But another very important aspect of finding truth is to ask what category the discussion falls into, in other words, look at the “big picture”, ask yourself “What is it”? What category does it fall into? For example, is the statement an opinion? Is it a claim to objective, universal truth? Or, in the case of the Bible, what is it? Is it basically a reliable book of history or does it contain hidden, individual, personal messages from God for the reader? Or, on the question of abortion, what is the fetus? Is it a growth of mere tissue? Is it simply part of the mother’s anatomy? or is it a genetically unique, individually complete human being? Often, before one can decide if something makes sense one has to know what category it falls into. This is also true in interpreting the Bible. One should ask what genre of literature are we looking at? Is the passage poetry, historical narrative, didactic teaching, advice, command, tied to some historic circumstance, applicable to all believers or specific to a particular situation?
One final example: Islam. What is it? Is it a religion like Christianity, Judaism, Buddhism (is Buddhism a religion?). What was Muhammed? Was he a prophet, charlatan, con artist or something else? Is Islam a political system, economic system, mind control cult or something else? Or is it a combination of all of these? Categories are very important when it comes to thinking. Figuring out what category something falls into is fundamental to thinking.
Putting people into categories is often a mistake. People are very complex, and categories are often very narrow and rigid. In critical thinking we are primarily interested in what the person is thinking and what a person is claiming to be true. Categories like “he is a consummate liar” or “she is undisciplined and unreliable” can be helpful but can also be simplistic and misleading.
Of course, as always, the thinking person will demand and give support for placing people and truth claims into any category. What is the evidence? What is the argument? What are the counter arguments? What is the minority report? And putting things into categories should not be done in haste. But we should always be thinking “What category does this person or claim fall into?”
Logic is almost synonymous with thinking. The “laws” of logic are built into the very language we use when communicating thought. So, knowing the fundamentals of logic is key to becoming a thinking person.
Formal logic, also known as deduction, is called formal because it has to do with the form of the argument. It is very closely tied to the concept of categories. We looked briefly into the importance of categories at the onset of our study. The study of formal logic is the study of propositions and the relationship between those propositions. A proposition is a “truth claim”. At its most basic level, formal logic consists of a claim that something is true. This particular claim is known as the conclusion. The conclusion is then supported by other propositions called premises, that are considered true and perhaps even obvious. The laws of logic consist of legitimate ways in which claims are related to each other. A conclusion supported by premises that are not related to the conclusion in a legitimate manner by some law of logic is considered unfounded or fallacious. The conclusion may actually be true. Even the premises can be true. But if there is no logical connection between premises and conclusion, the argument is considered unpersuasive (a non sequitur).
Example of the laws of logic: All men are mortal. Socrates in a man. Therefore, Socrates is mortal. In this classic example, “Socrates is mortal” is the conclusion. The claim that Socrates is mortal is supported by the claims that 1) Socrates is a man and 2) all men are mortal. This argument is sound. It conforms to the laws of logic. The reality of the claim may not be true in an absolute sense. For example, the claims that all men are mortal or that Socrates is a man may not be true. But if all men are mortal and if Socrates is a man then it would be absolutely certain that Socrates is mortal.
Our example illustrates a fundamental law of logic known as the hypothetical syllogism. The word syllogism is a rather fancy word but simply means a conclusion supported to two logically connected supporting claims. This syllogism has the form if A then B and if B then C. Therefore, if A then C. It would go like this: If Socrates is a man and if all men are mortal, then Socrates is mortal.
Every subject matter comes along with its own vocabulary. The cook knows what it means to baste a turkey. The football fan knows what “third and long” means. The seamstress knows what fabric bias is. And the person wanting to learn, use and discuss logic will find it helpful to learn the vocabulary of the study of logic. A good way to learn vocabulary is to use the new words in sentences, over and over again.
Here are some definitions:
- A proposition is a statement that asserts that something is objectively true.
- An objectively true statement is a statement about the object rather than the subject. The statement “I am hungry” is a statement about the speaker and is therefore not objective but subjective. The statement “Hunger is a constant, worldwide problem” is an objective statement. It is not about the speaker; it is about something in the world outside the speaker and which is either true or false for everyone. Logic is not and should not be applied to subjective statements. Subjective statements should not be confused with objective ones. Subjective statements are mere likes or dislikes, personal preferences or opinions where no claim to absolute, universal truth is being made. When someone makes a claim, it is very important to determine if the claim is subjective or objective. If it is subjective, it is mere opinion or personal preference and can make no claim on our allegiance or obedience.
- A conclusion is a proposition that is supposedly supported by evidence and reason. In a conversation, the listener is hoping to hear a conclusion, a clear statement of what the conversation is about and what is being said about what the conversation is about. When the listener or reader cannot discern the other persons conclusion, she often asks (or should ask) “what is your point?” In other words, “what are you talking about and what are you saying about what you are talking about?” Those questions should be followed up with a request for the supporting evidence, arguments and counter arguments.
- What the conversation is about is called the subject of the conclusion. What is being said about the subject is called the predicate. In the sentence “Owls are nocturnal predators”, the subject is “owls” and the predicate is “they are nocturnal predators”. Every proposition, whether conclusion or premise in an argument must have a subject and a predicate. If the subject and predicate are not clear, the listener should request clarification.
- Premises are propositions given in support of a conclusion. They are reasons why, in the mind of the speaker or writer, the conclusion should be believed. Premises are often referred to as assumptions. They are statements that are assumed to be true and perhaps even obvious. One should also require that the person making the truth claim give and defend their assumptions. When premises are tied to a conclusion in a manner consistent with some logical principle the conclusion and supporting premises are said to form an argument.
- So, an argument, in logic, is not a quarrel, it is a conclusion accompanied by supporting claims known as premises. The conclusion is tied to the premises by some known rule of logic.
It is good to know and use the proper vocabulary when doing logic. But even small children use logic without knowing the proper vocabulary. Here is a simplified explanation of thinking using logic: Thinking is knowing what is being discussed and exactly what is being said about it. Thinking is distinguishing between subjective feelings, opinions or personal preferences and claims that something is actually true, objectively true. Thinking is checking to see if what is being said or written is supported by evidence and statements that can be verified. Thinking is checking to see if the supporting claims are true and if they are relevant to the claim being made. If a person follows these simple principles, they are well on their way to finding truth, freedom, happiness, God and also helping others do the same.
For those with time and energy, here are three other logic forms in addition to the hypothetical syllogism that are very common to argumentation. They are modus ponens, modus tolens and the disjunctive syllogism. Surprisingly the “laws of logic” are very simple and even obvious. We use them every day. Even small children use them. They are part and parcel of everyday observation and conversation. They are how we think and talk. Yet they are very powerful tools and a great item to have in our “tool kit” for thinking critically. If the reader would prefer to simply stick to the basics and the general outline of formal logic this section can be skipped.
Modus Ponens goes like this: If A is true then B is true. A is true. Therefore, B is true. There are several ways to paraphrase this: A is sufficient to produce B or, every time we see A, we see B. Or A and B are inseparable. If you have A, you will have B also. Hey, we have A! Then we also have B. If A, then B, A, therefore B. Example: If we have gas fumes, oxygen and a spark, we will have an explosion. We have gas fumes, oxygen and a spark, look out!! We are about to have an explosion! Gas fumes, oxygen and a spark are sufficient to produce an explosion. The symbol A can contain various elements all joined together and simply called A.
In a similar way, in a case where if A is true then B must be true. But we find that B is not true, then A must not be true. In other words, if A always leads to B and B is not what we see in this case, then A must not have happened or was not the case. This form of argument is called Modus Tolens. In our example above, if a spark happens in the presence of gas fumes and oxygen then we will have an explosion. We had no explosion. Therefore, we did not have gas fumes, oxygen and a spark. Something was missing. No gas or no oxygen or no spark or perhaps none of the three (gas fumes, oxygen or a spark). Another example: If deficit government spending produces inflation and the government has been engaging in deficit spending, then we will have inflation. Modus Ponens: the government has been engaging in deficit spending. Result: We have experienced inflation. Modus Tolens: There has been no inflation! Therefore, government spending has not exceeded tax revenues.
Modus Ponens and Modus Tolens are very important logical forms from which we derive a method of argument. Some claims or combination of claims (the premises) are “sufficient” to prove a conclusion, that is, if they are true then the conclusion must be true, totally apart from any other evidence or claim. In other words, if A then B; A, therefore B, guaranteed.
Sometimes we hear someone say that something is not necessarily true. What they mean by that is that there are some exceptions to the rule. In other words, the premises are not sufficient to guarantee the conclusion every time. Then the question becomes, “What are the odds?” or “What are the circumstances that made the difference?”
Some claims are “necessary” for another claim to be true, that is, if that claim, the conclusion, is false, then the other claim or claims, the premises, must be false in part, at least. In other words, if A then B; not B, therefore, not A (in whole or in part).
The argument forms discussed above relate very much to the idea of cause and effect and answer the questions 1) are the premises sufficient to guarantee the conclusion? And 2) does the absence or negation of the conclusion demonstrate the absence or negation of the premises?
One final logical argument form is known as the disjunctive syllogism. It goes like this: A or B, not A, therefore B. Example: He either went to the gas station or he went to the bank. He didn’t go to the gas station. Oh, then he must have gone to the bank. If one of two options must be true, and one is false, then the other must be true. Although this logical form is completely valid, few situations lend themselves to an either/or interpretation. This latter observation often leads to what is called a false dilemma.
The False Dilemma
A false dilemma goes something like this: “Either he is uninformed, or he is lying!” No. He may be well informed but sincerely mistaken in his reasoning. There is a difference between someone being mistaken and someone intentionally misleading others. The false dilemma is often used to slander, shame or disqualify a person and has the proper logical form ( A or B, not A, therefore B), it is just presenting the argument as though there are no other options, other than the two given. In other words, A or B is not true. There may well be other options.
The Euthyphro dilemma is famous and goes like this: Euthyphro is one of Plato’s Dialogues in which something very similar to the following problem is presented: Is that which is good, good simply because God says so or is something good totally apart from God’s declaring it good? If the first is the case, then it seems that the “good” is just arbitrarily imposed by God and is not good in and of itself. If the second case is true, then God is superfluous to the “good” and not needed to explain or defend morality. The problem is a false dilemma because the two options given do not exhaust the options. The Christian response is that that which is good is defined by God’s very nature. It is not arbitrary but is just as much a part of reality as the physical universe itself.
One final note on logical forms. A contradiction in logic goes something like this: A is true, and A is not true. Example: “Mary saw an angel at the tomb of Jesus. Mary did not see any angel at the tomb of Jesus.” That would be a contradiction, the affirmation and negation of exactly the same identical claim. If one gospel writer, for example, says that she saw an angel and another gospel writer says she saw two angels there is no contradiction. If a third commentator fails to mention that Mary saw any angel at all at the tomb does not constitute a contradiction.
A contradiction is affirming and denying the exact same claim in the exact same manner and time and space. Many claims that the Bible is “full of contradictions” do not refer to contradictions at all. They are simply differences, which is perfectly normal. Different witnesses and different chroniclers of eyewitness testimony will include and exclude different details. As a matter of fact, if all witnesses and chroniclers of eyewitness testimony said exactly the same thing, one would suspect collusion or witness tampering. Differences are signs of authenticity, not of error or dishonesty in testimony.
Many criticisms of the Gospel accounts confuse differences in observations with contradictions. They are not contradictions unless they affirm and deny the exact same claim in the exact same way, space and time.
Argument by analogy
An analogy is a likeness drawn between two or more entities in one or more respects. Analogies are used in two manners that are often confused. One use of analogy is to use the similarity of something fairly well known and understood to something little known and little understood in order to show how the little known and unfamiliar entity could function or make sense or be of value or be dangerous. The parables of Jesus are examples of analogy used in this way. The second way analogy is used is as proof that something exists, how it functions, makes sense, is good or is dangerous. Analogies work very well in the first sense, that of making something unfamiliar more understandable without claiming that the analogy is a proof or forms an argument. Analogies are weak arguments when presented as proofs. But they are very effective aids in making the unfamiliar more understandable and accessible.
Note the difference between saying that 1) a watch, being obviously designed because of its complexity and specificity, can explain why many people believe that the universe could have been designed because the universe also demonstrates complexity and specificity and saying that 2) the complexity and specificity of a watch proves that the universe was designed. The watchmaker argument is used in an illustrative not probative manner. Atheists often claim that the “watchmaker argument” has been definitively refuted but refutation applies to arguments not to illustrations.
It can be very helpful to know the valid forms of logical argument. But what is most important is to understand that critical thinking consists of truth claims (not opinions or personal preferences) arranged in such a manner that one is the conclusion and the others (premises) are offered as support for the conclusion. The premises and the conclusion must be related to each other in some recognized logical relationship known as a law of logic (modus ponens for example) in order for the argument to be sound.
When discussing or debating any issue it is imperative that terms be properly defined and that the conclusion and premises be clearly stated. When they are not, one should ask “what is your point (conclusion)?” and what are your reasons (premises) for believing that conclusion. A third question is “have you looked at or considered alternative explanations or arguments?”
Note: The above discussion on logic forms relates specifically to deduction, sometimes called formal logic, since it deals with the form of an argument. Two other helpful methods of argumentation are induction and abduction. Induction deals with the probability of the conclusion being true based on data or research. Abduction is choosing the best explanation from among a set of possible explanations. Abductive arguments often consist of a combination of deductive and inductive argumentation.
Examples and Questions
Examples of non-arguments: Occasionally, people opposed to Christianity present what they think are arguments in defense or opposition to a particular position. Often their statements are not arguments at all. Recall that an argument consists of a conclusion supported by premises. Any position that fails to provide a clear conclusion and evidence and supporting propositions (premises) is not an argument at all. Here are some examples.
- The Bible is full or errors.
- More killing has been brought about by religion than anything else in history.
- Snakes don’t talk.
- God doesn’t answer prayer or didn’t answer my prayers.
- There is no evidence for belief in God.
- Only physical matter truly exists. There is no supernatural.
- “I believe in the twelve celestial, eternal spheres outside of the universe that provide the answers to true spirituality and everlasting bliss.”
All of the above examples fail the test of argumentation. Where is the evidence, the supporting statements and the logical connection? Let’s look at each one separately.
- The Bible is full or errors. Even if the Bible contained many errors, that would not in any way prove that God does not exist. The primary argument for God’s existence is the existence of the universe itself with all of its grandeur, order, specificity and fine tuning. And even if the Bible contained many errors, that would not logically prove that God did not appear to Abraham as related in Genesis 12 or that Jesus did not rise from the dead or that by his death he did not atone for our sins. Those claims have to be judged on their own merits, on the evidence, arguments and counter arguments in favor or against the claim itself. They cannot be dismissed simply because the Bible is assumed to be full of errors (a claim not well substantiated).
- More killing has been brought about by religion than anything else in history. Actually, more people have been killed in wars over territory and ideology than over religion. But even if it were true that many more had been killed over religion, that would not make Christianity false. Where is the argument? Where is the supporting data? What logical connection exists between people killing each other over religion, even over Christianity, and God’s existence?
- Snakes don’t talk. Here again the argument is incomplete. What conclusion can be drawn from the statement that (normally) snakes do not talk? The passage in Genesis 3 clearly states that the snake is Satan in snake form, not any ordinary snake out of the garden.
- God doesn’t answer prayer or didn’t answer my prayers. Again, what conclusion can be drawn from the fact that God did not answer (maybe never answers) prayer. Does that mean that God does not exist? He is a person with volition who decides what He will or will not do. God owes no one anything. Anything God grants, according to the Christian faith, is by grace (unmerited favor) and any punishment or ill that God withholds is by mercy. Grace and mercy are very fundamental concepts of the Christian faith. If God favorably answered every prayer uttered by his children it would make perfect sense for Christians to make their living at the expense of Las Vegas casinos and Christians would ace every test in school.
- There is no evidence for belief in God. This, of course is a subjective statement. What the person is saying is that “For me, there is insufficient evidence for belief in God”. But many others throughout history have found the evidence sufficient for belief. As a matter of fact, the vast majority of people and cultures throughout history have believed in some sort of deity. A small minority of people throughout history may have been atheists but that was their choice and has not been the majority opinion until modernity came into being. This is an excellent example of the importance of determining if the speaker is making a claim of objective, universal truth or just stating an opinion.
- Only physical matter truly exists. There is no supernatural. The claim that only physical matter exists is not a scientific statement, it is a philosophical assumption. It is a belief and the basis for atheism. There is no way that the existence of “spirit” or the non-material can be disproved by demanding that it manifest itself in material form, although Christianity claims that it did, indeed, do just that in the person of Jesus Christ of Nazareth and does so every day in the nature of free will, emotion, intelligence, goodness and evil. Most people believe they have a mind and free will and valid emotions that don’t lend themselves to explanation by purely physical, material means. Also, the claim that atheism is true because the non-material does not exist is “arguing in a circle”. It is saying the non-material does not exist because the non-material does not exist.
- “I believe in the twelve celestial, eternal spheres outside of the universe that provide the answers to true spirituality and everlasting bliss.” This seventh statement is just that, a statement. It is not an argument. No supporting statements or evidence have been given in support of it. People are free to believe it, of course, but no rational person should be persuaded to believe it.
I hope this concise and admittedly incomplete presentation on critical thinking has been helpful. As stated in the introduction, it is meant to be nothing more than a starter kit and a tool kit. Certainly, a more thorough study of formal logic and probability is called for. To that end a brief bibliography has been added to the conclusion of this article.
Copi and Cohen, Introduction to Logic, 11th Edition, Prentice Hall, Upper Saddle River, N.J., 2002
Koukl, Gregory, Tactics, Zondervan, Grand Rapids, MI, 2009
Wallace, J. Warner, Cold-Case Christianity, David C. Cook, Colorado Springs, CO, 2003
Singer, Margaret Thaler, Cults in Our Midst: The Hidden Menace in Our Everyday Lives, Jossey-Bass Publishers, San Francisco, 1995